A number of systems and programs are offered on the market for the design, the engineering and the manufacturing of objects. CAD is an acronym for Computer-Aided Design, e.g. it relates to software solutions for designing an object. CAE is an acronym for Computer-Aided Engineering, e.g. it relates to software solutions for simulating the physical behavior of a future product. CAM is an acronym for Computer-Aided Manufacturing, e.g. it relates to software solutions for defining manufacturing processes and operations. In such systems, the graphical user interface (GUI) plays an important role as regards the efficiency of the technique. These techniques may be embedded within Product Lifecycle Management (PLM) systems. PLM refers to a business strategy that helps companies to share product data, apply common processes, and leverage corporate knowledge for the development of products from conception to the end of their life, across the concept of extended enterprise.
The PLM solutions provided by Dassault Systemes (under the trademarks CATIA, ENOVIA and DELMIA) provide an Engineering Hub, which organizes product engineering knowledge, a Manufacturing Hub, which manages manufacturing engineering knowledge, and an Enterprise Hub which enables enterprise integrations and connections into both the Engineering and Manufacturing Hubs. All together the system delivers an open object model linking products, processes, resources to enable dynamic, knowledge-based product creation and decision support that drives optimized product definition, manufacturing preparation, production and service.
Some of these systems allow the representation of a modeled volume with a set of dexels. Several papers or patent documents notably suggest using dexel representation for machining simulation or interactive sculpting.
Examples of such documents are:                the paper entitled “A Virtual Sculpting System Based on Triple Dexel Models with Haptics”, Xiaobo Peng and Weihan Zhang, Computer-Aided Design and Applications, 2009;        the paper entitled “NC Milling Error Assessment and Tool Path Correction”,        
Yunching Huang and James H. Oliver, Proceedings of the 21st annual conference on Computer graphics and interactive techniques, 1994;                “Online Sculpting and Visualization of Multi-Dexel Volumes”, Heinrich Muller, Tobias Surmann, Marc Stautner, Frank Albersmann, Klaus Weinert, SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications;        the paper entitled “Virtual prototyping and manufacturing planning by using tridexel models and haptic force feedback”, Yongfu Ren, Susana K. Lai-Yuen and Yuan-Shin Lee, Virtual and Physical Prototyping, 2006;        the paper entitled “Simulation of NC machining based on the dexel model: A critical analysis”, Sabine Stifter, The International Journal of Advanced Manufacturing Technology, 1995;        the paper entitled “Real time simulation and visualization of NC milling processes for inhomogeneous materials on low-end graphics hardware”, Konig, A. H. and Groller, E., Computer Graphics International, 1998. Proceedings;        U.S. Pat. No. 5,710,709;        U.S. Pat. No. 7,747,418.        
GPGPU (General-Purpose computing on Graphics Processing Units) is the technique of using a graphic processing unit (GPU) which typically handles computation only for computer graphics, to perform computation in applications traditionally handled by the central processing unit (CPU). Some papers consider using the computation power of modern graphics processing units (GPU) for dexel representation. These papers make use of the LDNI (Layered Depth-Normal Images) algorithm, which is associated to a specific memory model.
Examples of such papers are:                the paper entitled “GPGPU-based Material Removal Simulation and Cutting Force Estimation”, B. Tukora and T. Szalay, CCP: 94: Proceedings Of The Seventh International Conference On Engineering Computational Technology;        the paper entitled “Layered Depth-Normal Images: a Sparse Implicit Representation of Solid Models”, Charlie C. L. Wang and Yong Chen, Proceedings of ASME international design engineering technical conferences. Brooklyn (N.Y.).        
Some authors suggest improving depth buffers models, which are the simplest incarnation of dexel models, by managing level of details with hierarchical grid refinements. This is notably suggested in the paper entitled “Real-time, dynamic level-of-detail management for three-axis NC milling simulation”, by S. Q. Liu, S. K. Ong, Y. P. Chen, A. Y. C. Nee.
However, the solutions listed above lack efficiency, notably from a user utilization point of view. Within this context, there is still a need for an improved solution for designing a modeled volume represented by a set of dexels.